3 ms·
The radius of the sphere, assuming the cube has side length 1, is (sqrt(D)-1)/2. It seems worthy of note that this radius becomes arbitrarily large.
by scythe 5y ago
The radius of the sphere, assuming the cube has side length 1, is (sqrt(D)-1)/2. It seems worthy of note that this radius becomes arbitrarily large.
- kgwgk 5y agoAnd the distance from a vertex of the unit cube to the center is sqrt(D)/2, which also becomes arbitrarily large. https://www.math.ucdavis.edu/~strohmer/courses/180BigData/180lecture1.pdf https://www.math.ucdavis.edu/~strohmer/courses/180BigData/18... > The result, when projected in two dimensions no longer appears convex, however all hypercubes are convex. This is part of the strangeness of higher dimensions - hypercubes are both convex and “pointy.”
- AnimalMuppet 5y agoIsn't it more accurate to say that hypercubes are convex and their projections are pointy?
- deleted 5y ago[deleted]
- kgwgk 5y agoYes. Hence the quotes, I guess. But hyperspheres are convex and their projections are also convex. So it's not really appropriate either to say that they are "spiky" as in https://news.ycombinator.com/item?id=29969613 https://news.ycombinator.com/item?id=29969613